1. Field of the Invention
This invention relates to methods and systems of estimating the likely binding affinity between molecular entities.
2. Description of the Related Art
A wide variety of techniques for determining the energetically favored interaction geometry between two interacting molecules have been developed. In addition, once this geometry has been determined, it is often useful to further predict the binding affinity, generally expressed as the pKi, of the molecules in solution. This is useful, for example, in the drug discovery process, where it is highly desirable to be able to computationally evaluate the likely effectiveness of a drug candidate compound without the need for wet chemical testing of the compound.
Various methods have been devised for estimating the likely binding affinity between chemical entities such as a drug candidate molecule (e.g., a ligand) and a protein or other form of receptor. Some methods use a mathematical model of the form:
pKi=xcexa3jCjDj
wherein Cj are constant coefficients, and Dj are calculated ligand-protein interaction descriptors which depend on the nature of the ligand-protein interaction (e.g. 3-D binding geometry, computed binding energies, etc.) for the specific ligand-protein system for which the pKi is being predicted.
To use the above-described method, a set of descriptors are selected which are believed to be related to binding affinity. The constant coefficients may be selected by well-known regression methods using a training set of systems whose binding affinities have been determined by experiment, and whose three-dimensional structures have also already been experimentally determined or derived computationally. In these modeling techniques, even though the true relationship between the pKi of a selected system and each of the descriptors may be poorly understood and non-linear, it is hoped that a linear combination of carefully selected descriptors can be a useful and relatively accurate predictor of pKi values.
Since many descriptors are available to be included in the above formula, it is possible to xe2x80x9cover-fitxe2x80x9d the training data with a large number of descriptors, in order to at least artificially fit the given training data with the many descriptors. However, if the descriptors and coefficients do not adequately reflect physical reality, then descriptors and coefficients that fit one set of training data may not fit another set of training data. Moreover, using a large number of descriptors results in a complex and difficult to understand prediction model which is often not particularly useful when applied to other systems outside the set of training data. Using a large number of descriptors also requires more computational power.
It is thus difficult to determine what set of descriptors will produce a robust and accurate model. As noted briefly above, the correlation between pKi and the atomic features of interacting molecules is very complex and generally non-linear, and the descriptors used to characterize these atomic features can take an essentially infinite number of forms. In addition, the descriptors may be interelated in physical significance, and may affect pKi in different ways depending on the types of interacting molecules.
It would thus be advantageous for the drug discovery process as well as other applications to devise descriptors for use in linear formulas for the prediction of binding affinity that result in models having relatively wide applicability and good predictive accuracy.
In one embodiment, the invention comprises a method of estimating a binding affinity between first and second interacting molecular entities. The method may comprise defining at least one surface area descriptor of the interaction, the descriptor comprising an amount of non-neutral surface area of the first molecular entity that is proximate to a non-neutral portion of the second molecular entity and using the amount of non-neutral surface area of the first molecular entity in a formula for numerically estimating the binding affinity.
In another embodiment, a method of predicting binding affinity between two molecular entities comprises determining a van der Waals interaction energy between the first molecule and the second molecule (the vdW value), determining a surface area of the first molecule forming complimentary polar interactions with the second molecule (the Att_pol value), determining a surface contact area of the first molecule forming uncomplimentary polar interactions with the second molecule (the Rep_pol value), calculating a value of pKi at least using a formula pKi=C0+(C1*vdW)+(C2*Att_pol)+(C3*((Att_pol*Att_pol)+(Rep_pol*Rep_pol))), based on the determined values of vdW, Att_pol, and Rep_pol, with C0, C1, C2 and C3 being constant coefficients.